{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "61b10fe5-d1bd-43ee-8efb-d9ce2d579a3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<function chebfit at 0x7f09a8776c00>\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.polynomial.chebyshev import chebfit, chebval\n",
    "plt.rcParams['axes.unicode_minus']=False#用来正常显示负号\n",
    "plt.rcParams['font.sans-serif']=['SimHei']#用来\n",
    "# 定义要逼近的函数\n",
    "def f(x):\n",
    "    return np.sin(x)\n",
    "\n",
    "# 生成 x 值范围\n",
    "x = np.linspace(-1, 1, 100)\n",
    "\n",
    "# 使用切比雪夫多项式逼近\n",
    "degree = 4  # 选择逼近的多项式的阶数\n",
    "cheb_coeffs = chebfit(x, f(x), degree)\n",
    "print(chebfit)\n",
    "\n",
    "# 使用得到的切比雪夫系数计算逼近值\n",
    "f_approx = chebval(x, cheb_coeffs)\n",
    "\n",
    "# 绘图对比原始函数和逼近结果\n",
    "plt.plot(x, f(x), label='Original Function')\n",
    "plt.plot(x, f_approx, label=f'Chebyshev Approximation (degree={degree})')\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.title('Chebyshev Polynomial Approximation of sin(x)')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b15742fa-7ea9-4cca-9858-5402fd9deda3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7984acfb-cb42-4cdc-914b-9cc5077de020",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dc1ec2b8-8b09-429e-8bf1-9d98ccf25057",
   "metadata": {},
   "outputs": [],
   "source": []
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